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II TABLE I. - Tangents and Externals to a P Curve. <br />Chord=100 ft. - <br />Angle <br />Tangent <br />External <br />Angle <br />Tangent <br />External <br />Angle <br />Tangent <br />External <br />1° <br />50.00 <br />:22 <br />8° <br />400.66 <br />13.99 <br />16° <br />754.32 <br />49.44 <br />10' <br />58.34 <br />.30 <br />-10' <br />409.03 <br />14.58 <br />10' <br />•762.80 <br />50.55 <br />20 <br />66.67 <br />_ .39' <br />20 <br />417.41 <br />15.18 <br />20 <br />'771.29- <br />'51.68 <br />30 <br />75.01 <br />.49 <br />30 <br />.425.79 <br />15.80 <br />30 <br />779.77 <br />52.82 <br />40 <br />83.34 <br />.61 <br />40 <br />434.17 <br />16.43 <br />40. <br />788.26 <br />53.97 <br />50 <br />91.68 <br />.73 <br />50 <br />442.55 <br />17.07 <br />50 <br />796.75 <br />55.13 <br />2 <br />100.01 <br />.87 <br />9 <br />450.93. <br />17.72 <br />16 <br />805.25 <br />56.31 <br />10 <br />.108.35 <br />1.02 <br />10 <br />459.32' <br />18.38 <br />10- <br />813.75 <br />• 57.50 <br />20 <br />116.68 <br />1.19 <br />'. 20 <br />:467.71 <br />•19.06 <br />•20 <br />822.25 <br />58.70. <br />30 <br />.125.02 <br />1.36 <br />30 <br />'476.10 <br />19.75 <br />30 <br />830.76 <br />59.91 <br />40 ' <br />133.36 <br />1.55 <br />40 . <br />'434.49 <br />20.45 <br />40 <br />839.27' <br />61.14 <br />50 <br />1'41.70 <br />1.75 <br />50 <br />:492.88 <br />21.16 <br />50 <br />847.78 <br />62.88 <br />8 " <br />150.04 <br />1.96 <br />10' <br />501.28 <br />21•.89 <br />".17 ' <br />856.30 <br />63.63 <br />10 <br />158.38 <br />2.19 <br />10 <br />509.68 <br />22.62 <br />10 <br />864.82. <br />.64.90 <br />20 <br />166.72 <br />2.43 <br />20 <br />518.08 <br />'.23.38 <br />20 <br />873.35 <br />66.18 <br />30 <br />175.06 <br />2.67 <br />30 <br />526.48 <br />24.14 <br />30 <br />881.88 <br />67.47 <br />40 <br />183.40 <br />2.93 <br />40 <br />534.89 <br />24.91 <br />40 <br />890.41 <br />63.77 <br />50 <br />191.74 <br />3.21 <br />50 <br />543`29 <br />25.70 <br />50. <br />898.95 <br />70.09 <br />4 <br />200.08 <br />3.49. <br />11 <br />551.70 <br />26.50 <br />18 <br />907.`49 <br />71.42 <br />10 <br />208.43 <br />3.79 <br />10 <br />560.11 <br />27.31 <br />10 <br />916.03 <br />72.76 <br />20 <br />216.77 <br />4110 <br />20 <br />56S.53 565.53 <br />024.58 <br />74.12 <br />30 <br />225.12 <br />4'.42 <br />:. 30 <br />576.95 <br />.28.14. <br />28.97 <br />•20 <br />30 <br />933.13 <br />75.49 <br />40 <br />233.47 <br />4.76 <br />40 ' <br />585.36 <br />29.82 <br />40 <br />041.69 <br />76.86 <br />60 <br />241.81 <br />5.10 <br />50 <br />593.79 <br />30:68. <br />50 <br />950.25 <br />78.26 <br />5 <br />250.16 <br />5.46 <br />12 <br />602.21 <br />31.56 <br />19 <br />958.81 <br />79.67 <br />10 <br />258.51 <br />5.83 <br />" 10 <br />610:64 <br />32:45- <br />10 <br />067.38. <br />81.09 <br />20 <br />266.86 <br />6.21 <br />20 <br />.,619.07 <br />33.35 <br />20 <br />975.96 <br />82.53 <br />30 <br />275.21 <br />6:61 <br />30 <br />627.50 <br />34.26 <br />30 <br />984.53 <br />83.97 <br />40 <br />283.57 <br />7.01 <br />,. 40 <br />635.03 <br />35.18 <br />40., <br />993.12 <br />85.43 <br />50 <br />291.92 <br />7.43 <br />50 <br />644.37 <br />36.12 <br />50," <br />1001.7 <br />86.90 <br />6 <br />300.28' <br />7.86 <br />13 : -.` <br />652.81 <br />37.07 <br />20 - <br />1010.3 <br />88.39 <br />10 <br />308.64 <br />8.31 <br />10 <br />661'.25 <br />38.03 <br />10 <br />1018.9 <br />89.89 <br />20 <br />316.99 <br />8.76 <br />20 <br />669'.70 <br />39.01 <br />20 <br />1027.5 <br />91.40 <br />30 <br />:325.35' <br />- 9.23 <br />30 <br />678.15 <br />39.99 <br />30 <br />1036:1 <br />02.92 <br />40 <br />:.333.71 <br />9.71 <br />40 <br />686.60 <br />40.99 <br />40 <br />1044.7 <br />94.46 <br />50 <br />342.08 <br />10.20 <br />50 <br />695.06 <br />42.00 <br />50 <br />1053.3 <br />96.01 <br />7 <br />350.44 <br />10.71 <br />14 <br />703.51, <br />-43.03 <br />21 <br />1061.9 <br />97.57 <br />10 <br />358.81 <br />' 11.22 <br />10 <br />711.97 <br />" 44.07 <br />10 <br />1070.6 <br />99.16 <br />20 <br />367.17' <br />'. 11.75' <br />20_ <br />720:44. <br />-45:12 <br />20 <br />.1079.2 <br />100.75 <br />30 <br />375.54 <br />12.29 <br />30 <br />728.90 <br />46.13 <br />30 <br />1087.8 <br />102.35 <br />40 <br />383.91 <br />12.85 <br />40 <br />737:37 <br />47.25 <br />40 <br />1096.4 <br />103:97 <br />50 <br />392.28 <br />13.41 <br />50,. <br />745.85 <br />• 48.34 <br />1 50 <br />1105.1 <br />1 105.60 <br />Corrections to be Added "(T =Tangent. E =External.) <br />Int. <br />Angle <br />Curve 5° <br />10° 15° 20° <br />25° <br />30° 35° 40° <br />_ <br />45° 500 <br />556 <br />60° <br />65° <br />706 <br />5° <br />T=.02 <br />.03 .05 .06' <br />.08 <br />.10 .I1 .13 <br />.15 , .16 <br />.18 <br />.20 <br />.21 <br />.23 <br />E =.000 <br />.000 .001 .001 <br />.002 <br />.002 .002 .003 <br />.003 .004 <br />.004 <br />.004 <br />.005 <br />.005 <br />loo <br />T=:03 <br />.06 .09 .13 <br />'.16 <br />.19 ..22 .25 <br />.28 .31 <br />..34 <br />.38 <br />.42 <br />.46 <br />E =.001 <br />.003 .004 ..006 <br />.007 <br />.008 .009 .011 <br />.012 .014 <br />.015 <br />.017 <br />.018 <br />.020 <br />15o <br />T=.04 <br />.10 .14 .19 <br />.24 <br />.29 .34 .39 <br />.45 .51 <br />.53 <br />.58 <br />..63 <br />.68 <br />E=.003 <br />".007r.0101-014 <br />.018 <br />.023 .027 .029 <br />.032 .035 <br />.039 <br />.043 <br />.047 <br />.051 <br />20o <br />T= .06 <br />.13 .19 .26 <br />.32 <br />.39 .45 .51 <br />.58 .65 <br />.72 <br />.79 <br />.84 <br />E =.006 <br />.011 .017 .022 <br />.028 <br />.034 .038 .045 <br />.051 .057 <br />.063 <br />.070 <br />.076 <br />256 <br />T=.08 <br />.16 .24 .33 <br />.40 <br />.49 .58 G7 <br />.75 .83 <br />.90 <br />.99 <br />1.06 <br />1. <br />E=.009 <br />.018 .027 .038 <br />.046 <br />.056 .085 .074 <br />.083 .093 <br />.106 <br />.120 <br />..127 <br />9Q <br />083 <br />TABLE I. -.Tangents and Externals to a 1° Curve. IIY <br />Chord =100 ft. <br />• Int. Tangent 'External Int. Tangent External Int' Tangent External <br />Angle Angle Angle <br />X22°', 1113.7 107.24 29° 1481.8 188.51 38° 1861.7 294.9 <br />11'22.4 108.90 10' 1490.7 190.74 10' 1870.9 297.7 <br />20 1131.0 110.57 ; 20 1499.6 192.99 20 1830.1 300.8 <br />30 1139.7 112.25 -30 1505.5 195.25 30 1889.4 303.5 <br />•40 1148.4 113.95 40 1517.4 197.53 40 1898.6 308.4 <br />50 1157.0 115.66 50 1526.3 199.52 50 1907.9 309.3 <br />23'' ,1165.7 117.38 30" 1535.3 202.12 37 1917.1 312.2 <br />10 1174.4 110.12 10 1544.2 204.44 10 1926.4 315.2 <br />20 . 1133.1 120.87 20 1553.1 '108.77 20 1935.7 318.1 <br />30 1191.8 122.63 30 1562.1 209.12 30 1945.0 321.1 <br />' 40 1200.5 124.41 40 1571.0 211.48 40 1954.3 324.1 <br />• 50 1209.2 126.20 50 1550.0 213.86 50 1963.6 327.1 <br />,.24 1217.9 123.00 31- 1559:0, "216.3 38 .1972.9 330.2 <br />10 12`26.6 120.82 10 15980 ,218.7 10 1932.2 333.2 <br />20 1235.3 131 65 20 1606:9• '221.1 20 1991.5 336.3 <br />30 : 1244.0 133.50 30 ;.1615.9' 223.5 30 -.2000.9 339.3 <br />•"'40 .1252.8 135.35 40 1624.9 226.0 40 2010.2 342.4 <br />50 ` 1261.5 137.23 50 ! 1633.9 228.4 50 2019.6 345.5 <br />1 <br />25 . 1270.2 139.11 32 1643.0• 230.9 39 2029.0 .348.8 <br />" 10 1279.0 141.01 10 1852.0 233.4 10 2038.4 351.8 <br />' 20 1257.7' 142.93 20 1661.0 235.9 ' 20 2047.8 354.9 <br />30 1296.5 144.55 30 1670.0 238.4 30 2057.2 358.1 <br />.40 1305.3 146.79 40 , 1679.1 241.0 40 2066.8 361.3 <br />` <br />50 � 1314,0 148.75 " 50 '1688.1 243.5 50 •2076.0 364.5 <br />28 1322.8 150.71 33 1897:2 246.1 , .40 2085.4 367.7 <br />'10 1331.6 152.69 .10 1706.3 248.7 ' _10 2094.9 371.0 <br />..20 1340.4 154.69 "20 1715.3 251.3 20 2104.3 374.2 <br />..30 � 1349.2 156.70 '" 30 1724.4 253.9 `. 30 2113.3 377.5 <br />40 1355.0, 158.72 -'40 1733.5 256.5 40 � 2123.3 330.8 <br />-"b0 � 1386.81 160.76 50 1742.6 259.1 50 ••'2132.7 " 384.1- <br />27 <br />84.1 <br />27 ' 1375:6 162.81 34 1751.7 261.3 41, 2142.2 387.4 <br />'. 10 1384.4 164.56 '10 1760.8 264.5 10 2151.7 390.7 <br />20 .'1393.2 166.95 20 .'1770.0 267.2 20 2161.2 394.1 <br />'30 1402.0; 169.04 ' 30 '1779.1 269.9 1 30 2170.8 397.4 <br />' 40 1410.9 171.15 40 1758.2 272.6 ' 40 2150.3 400.8 <br />' 50 1419.7 173.27 50 1797.4 275.3 50 2189.9 404.2 <br />28 1428.6 175.41. 35 1806.6 278:1 42 2199.4 407.6 <br />10 1437.4 177.55 10 1515.7 280.5 10 2209.0 411.1 <br />20, 1446.3 179.72 20 '1824.9 283.6 20 2218.6 " 414.5 <br />30 1455.1 181.8 <br />14 <br />13b • <br />As <br />Corrections to be Added- (T =Tangent: 'E =External.) <br />Int. Curve S° 10° 15°' 20° 25°' 30° 35° 40° 45° 50° 55° 60° 65° 700 <br />Angle <br />200 T=.06 .13 .19 .26 .32 .39 .45 .61 .58 .65 .72 .79 .84 .90 <br />E=.008 .011 .017 .022 .028 .034 .038 .045 .O.il .057 .063 .070 .076 .033 <br />25° T=.08 .16 .24 .33 .40 .49 .58 .67 .75 .83 .90 .99 1.06 1.14 <br />E=.009 .018 .027 .036 .046 .056 .065 .074 .083 .093 .106 .120 .127 .135 <br />30° T=.10 .19 .29 .39 .49 .59 .69 .79 .89 .99 1.09 1.20 1.29 1.39 <br />- <br />E=.013 .025 .038 .O,il .065 .078 .090 .103 .116 .129 .149 .170 .179 .188 <br />35° T=.11 .22 .34 .47 .58 .69 .80 .93 ].OS 1.17 1.29 1.42 1.54 1.86 <br />E =.018 .035 .054 .072 .086 .109 .131 .153 .175 .197 .213 .230 .247 .284 <br />400 T=.13 � .26 .40 :'0931 <br />5 .67 .80 .93 1.Q6 1.20 1.34 1.49 1.64 1.79 1.94 <br />E =.023 .046 .070 .093 .117 .141 .172 .203 .234 .265 .277 X90 .315 .341 <br />450 T=.15 .30 .44 .60 .76 .91 1.OG 1.21 1.37 1.52 1.70 1.87 2.04 2.21 <br />E=.030 <br />.060 <br />.093 <br />.119 <br />.153 <br />.184 <br />.21E <br />.254 .239 <br />.325 <br />.351 <br />.378 <br />.411 <br />.445 <br />9 <br />30 <br />1834.1 <br />256.4 <br />30 <br />2228.1 <br />418.0 <br />40 <br />1464.0 <br />184.08 <br />40 <br />1843.3 <br />289.2 <br />4D <br />2237:7 <br />421.4 <br />-'•-50 ' <br />1472.9 <br />136.29 <br />,50 <br />1852.5. <br />292.0 <br />'50 <br />2247.3 <br />425.0 <br />14 <br />13b • <br />As <br />Corrections to be Added- (T =Tangent: 'E =External.) <br />Int. Curve S° 10° 15°' 20° 25°' 30° 35° 40° 45° 50° 55° 60° 65° 700 <br />Angle <br />200 T=.06 .13 .19 .26 .32 .39 .45 .61 .58 .65 .72 .79 .84 .90 <br />E=.008 .011 .017 .022 .028 .034 .038 .045 .O.il .057 .063 .070 .076 .033 <br />25° T=.08 .16 .24 .33 .40 .49 .58 .67 .75 .83 .90 .99 1.06 1.14 <br />E=.009 .018 .027 .036 .046 .056 .065 .074 .083 .093 .106 .120 .127 .135 <br />30° T=.10 .19 .29 .39 .49 .59 .69 .79 .89 .99 1.09 1.20 1.29 1.39 <br />- <br />E=.013 .025 .038 .O,il .065 .078 .090 .103 .116 .129 .149 .170 .179 .188 <br />35° T=.11 .22 .34 .47 .58 .69 .80 .93 ].OS 1.17 1.29 1.42 1.54 1.86 <br />E =.018 .035 .054 .072 .086 .109 .131 .153 .175 .197 .213 .230 .247 .284 <br />400 T=.13 � .26 .40 :'0931 <br />5 .67 .80 .93 1.Q6 1.20 1.34 1.49 1.64 1.79 1.94 <br />E =.023 .046 .070 .093 .117 .141 .172 .203 .234 .265 .277 X90 .315 .341 <br />450 T=.15 .30 .44 .60 .76 .91 1.OG 1.21 1.37 1.52 1.70 1.87 2.04 2.21 <br />E=.030 <br />.060 <br />.093 <br />.119 <br />.153 <br />.184 <br />.21E <br />.254 .239 <br />.325 <br />.351 <br />.378 <br />.411 <br />.445 <br />